Determine the shear stress in each section - cells, Mechanical Engineering

Assignment Help:

Determine the shear stress in each section - cells:

In Figure, the mean dimensions of the two cells are 100 mm × 50 mm and 50 mm square.

t1 = 3 mm,       t2 = 6 mm,       t3 = 3 mm

1996_Determine the shear stress in each section.png

Figure

Determine the shear stress in each section, and the angle of twist per metre length for a torque of 3000 Nm. G = 80,000 N/mm2.

Solution

A1  = (100 × 50) = 5000 mm2

A2  = 50 × 50 = 2500 mm2

Z1  = (2 × 100) + 50 = 250 mm

Z 2  = (2 × 50) + 50 = 150 mm

Z3  = 50 mm

τ1 t1  = τ2 t2  + τ3 t3

⇒         τ1 × 3 = τ2 × 6 + τ3 × 3

3 τ1 = 6 τ2  + 3 τ3             ---------- (1)

T = 2 (τ1 t1 A1  + τ2 t2 A2 )

⇒         3000 × 103  = 2 [τ1 × 3 × 3000 + τ2 × 6 × 2500]

⇒         τ1 + τ2  = 50            -------- (2)

 

1 Z1 + τ3 Z3 ) / A1 = (τ2 Z2 - τ3 Z3 )/A2                  

 (τ1 × 250 + τ3 × 50) /5000= (τ2 × 150 - τ3 × 50)/ 2500

⇒         5 τ1 + τ3  = 6 τ2  - 2 τ3

⇒         5 τ1 = 6 τ2  - 3 τ3                                           ------------ (3)

 (3) - (1) ⇒ 2 τ1 = - 6 τ3

τ1 = - 3 τ3                 ---------- (4)

From (1),

3 (- 3τ3 ) = 6 τ2  + 3 τ3

τ2  = - 2 τ3

From (2),

- 3 τ3  - 2 τ3  = 50     --------- (5)

τ3  = - 10 N/mm2

τ1 = - 3 (- 10) = 30 N/mm2

τ2  = - 2 (- 10) = 20 N/mm2

∴          θ= (τ1 Z1 + τ3 Z3 ) l /2G A1 ,      Here  l = 1000 mm

= [30 × 250 + (- 10) × 50]/ (2 × 80 × 103 × 5000) × 1000

= 8.75 × 10- 3 radians


Related Discussions:- Determine the shear stress in each section - cells

Calculate amplitude of vibration of machine, A machine of mass one tonne is...

A machine of mass one tonne is acted upon by an external force of 3000 N at a frequency of 1500 rpm. To reduce the effects of vibration, isolator of rubber having a static deflecti

Determine the maximum value of the coefficient of friction, Determine the m...

Determine the maximum value of the coefficient of friction: A force of 200 N inclined at 60 o to the horizontal is applied to the block A weighing 400 N. find out whether blo

Compton effect, Explain compton effect snd its significance

Explain compton effect snd its significance

Relation for fin insulated tip and the heat dissipation, Derive the relatio...

Derive the relation for a fin insulated at the tip and the heat dissipation?

Casting, causes and remedy of coldshut,misruns,shirnkage cavity,microporosi...

causes and remedy of coldshut,misruns,shirnkage cavity,microporosity,metal penetration,mismatch

Evaluate the power output of turbine, Evaluate the power output of turbine:...

Evaluate the power output of turbine: Q: A turbine in steam power plant operating under steady state conditions receives the superheated steam at 3MPa and 350ºC at the rate o

Fluid Mechanics, temperature lapse rate differentiation integration...

temperature lapse rate differentiation integration...

Angular speed of the cylinder, Angular speed of the cylinder: A cylind...

Angular speed of the cylinder: A cylinder of mass 70 kg rotates from rest in frictionless bearing under the action of a mass of 7.0 kg carried by a rope wrapped around the cyl

Where a and b are positive constants, Assume the production function is giv...

Assume the production function is given by the following equation (where a and b are positive constants): Q = aL+bK. What is the marginal rate of technical substitution of labor fo

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd